Problem: Solve for $x$ and $y$ using elimination. ${x+3y = 11}$ ${-x+2y = -6}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $5y = 5$ $\dfrac{5y}{{5}} = \dfrac{5}{{5}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x+3y = 11}\thinspace$ to find $x$ ${x + 3}{(1)}{= 11}$ $x+3 = 11$ $x+3{-3} = 11{-3}$ ${x = 8}$ You can also plug ${y = 1}$ into $\thinspace {-x+2y = -6}\thinspace$ and get the same answer for $x$ : ${-x + 2}{(1)}{= -6}$ ${x = 8}$